Answer:
v = 28.7 m/s
Explanation:
- According to the Work Energy Theorem, the work done by external forces on the system, is equal to the change in the kinetic energy of the system.
- In absence of friction, the only force that does work , producing a displacement in the direction of the force, is the component of gravity parallel to the slide:
- The displacement d,along the slide, can be found from the definition of the sine of an angle, as follows:
- Solving for d, we get:
- Now, the work done by Fgp, is just the product of the force times the displacement, as follows:
- From (1) and (2) we can find W as follows:
- This expression must be equal to ΔK, as follows:
- Simplifying common terms, we can solve for v (the velocity of the sled at the bottom of the slide), as follows:
- The velocity of the sled at the bottom of the slide is 28.7 m/s, taking as positive the direction down the slide.